Respuesta :
Answer:
Carlos pay in service charges is $1721.3
Step-by-step explanation:
Given : Carlos took seven years to pay off his loan by making identical quarterly payments.
The loan had a principal of $22,375 and 5.49% interest, compounded quarterly.
Carlos paid a total of $28,821.67.
To find : How much did Carlos pay in service charges?
Solution : First we find the monthly payment of the loan
Formula of monthly payment
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $22,375
Rate r= 5.49%=0.0549 compounded quarterly
[tex]i=\frac{0.0549}{4}=0.013725[/tex]
Time = 7 years
[tex]n=7\times4=28[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.013725)^{-28}}{0.013725}[/tex]
[tex]D=\frac{1-(1.013725)^{-28}}{0.013725}[/tex]
[tex]D=\frac{1-0.68270}{0.013725}[/tex]
[tex]D=\frac{0.3172}{0.013725}[/tex]
[tex]D=23.1177[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{22375}{23.1177}[/tex]
[tex]M=967.871[/tex]
Now payment he has for for 7 years compounded quarterly i.e, for 28
Payment = 967.871 × 28 = $27100.39
Service charges = Total payment - payment
= $28,821.67 - $27100.39
= $1721.27
Therefore, Carlos pay in service charges is $1721.3
